Summary The human zona pellucida is composed of four glycoproteins (ZP1, ZP2, ZP3, and ZP4) and has an important role in reproduction. Here we describe a form of infertility with an autosomal recessive mode of inheritance, characterized by abnormal eggs that lack a zona pellucida. We identified a homozygous frameshift mutation in ZP1 in six family members. In vitro studies showed that defective ZP1 proteins and normal ZP3 proteins colocalized throughout the cells and were not expressed at the cell surface, suggesting that the aberrant ZP1 results in the sequestration of ZP3 in the cytoplasm, thereby preventing the formation of the zona pellucida around the oocyte.

Let K be a field of characteristic 0 containing all roots of unity. We classified all the Hopf structures on monomial K-coalgebras, or, in dual version, on monomial K-algebras.  2004 Elsevier Inc. All rights reserved.

In this study, we synthesized novel gold-carbon dots (GCDs) with unique properties by microwave-assisted method. The characterization of high-resolution transmission electron microscope (HRTEM), XRD, high-angle annular dark field scanning transmission electron microscope (HAADF-STEM), and energy dispersive spectrometer demonstrates that GCDs are composed of carbon and Au. Tiny Au clusters are dispersed in a 2 nm-size carbon skeleton, which integrates the properties of typical CDs and gold nanoclusters (AuNCs), displaying fascinating peroxidase-like activity and single excitation/dual emission. Dual emission of the GCDs exhibits different fluorescent response to the target species and enables the GCDs to be exploited for sensing and bioimaging. The highly photostable and biocompatible GCDs were applied to dual fluorescent imaging for breast cancer cells and normal rat osteoblast cells under a single excitation. Moreover, ratiometric fluorescence imaging was used to monitor Fe(3+) level in normal rat osteoblast cells.

We provide a quiver setting for quasi-Hopf algebras, generalizing the Hopf quiver theory. As applications we obtain some general structure theorems, in particular the quasi-Hopf analogue of the Cartier theorem and the Cartier-Gabriel decomposition theorem. IntroductionThe notion of quasi-Hopf algebras was introduced by Drinfeld [9] in connection with the Knizhnik-Zamolodchikov system of equations. It is obtained from that of Hopf algebras by a weakening of the coassociativity axiom.Quasi-Hopf algebras turn out to be very useful in various areas of mathematics and physics such as low-dimensional topology, number theory, integrable systems, and conformal field theory.Quivers are oriented graphs consisting of vertices and arrows. They are widely used in many areas of mathematics and physics. In particular thanks to their combinatorial behavior, quivers are very powerful in the investigation of algebraic structures and representation theory.We propose to carry out a systematic study of elementary quasi-Hopf algebras and pointed dual quasi-Hopf algebras [16] by taking advantage of quiver techniques (see e.g. [2]). The goal of the present paper is to provide a handy quiver setting. For a wider setting and the convenience of exposition, we work mainly with dual quasi-Hopf algebras. A standard dualisation process will give the corresponding results for quasi-Hopf algebras. To avoid too many dual's and quasi's we use the term "Majid algebra" for "dual quasi-Hopf algebra", which was proposed by Shnider-Sternberg [22]. 1 Throughout, we work over a field k. We show in Section 3 that the path coalgebra kQ of a quiver Q admits a Majid algebra structure if and only if Q is a Hopf quiver [7], and that any coradically graded pointed Majid algebra H can be embedded into a Majid algebra structure on the path coalgebra of some unique Hopf quiver Q(H) determined completely by H.This generalizes the quiver setting for Hopf algebras [6,7,11,25] into the broader class of quasi-Hopf algebras. As applications we obtain some general structure theorems in Section 4, namely the quasi-Hopf analogue of the Cartier theorem and the Cartier-Gabriel decomposition theorem for Hopf algebras (see e.g. [4,18,24]). In particular we show that a cocommutative connected Majid algebra over a field of characteristic zero is isomorphic to the universal enveloping algebra of a Lie algebra, which indicates that there is no cocommutative connected Majid algebra out of the usual Hopf setting.

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Asymmetry of quantum states is a useful resource in applications such as quantum metrology, quantum communication, and reference frame alignment. However, asymmetry of a state tends to be degraded in physical scenarios where environment-induced noise is described by covariant operations, e.g., open systems constrained by superselection rules, and such degradations weaken the abilities of the state to implement quantum information processing tasks. In this paper, we investigate under which dynamical conditions asymmetry of a state is totally unaffected by the noise described by covariant operations. We find that all asymmetry measures are frozen for a state under a covariant operation if and only if the relative entropy of asymmetry is frozen for the state. Our finding reveals the existence of universal freezing of asymmetry, and provides a necessary and sufficient condition under which asymmetry is totally unaffected by the noise.Symmetry is a central concept in quantum mechanics, describing invariant features of a quantum system with respect to the action of a group of transformations [1]. For a specific symmetry, two relevant notions are asymmetric states and covariant operations, which are the states that break the symmetry and the quantum operations that respect the symmetry, respectively. In the physical world, all elementary interactions are expected to have specific symmetries [2]. For example, the interactions that do not have preferred direction are rotationally invariant and hence have SO(3) symmetry. The presence of a symmetry in a system generally imposes restrictions on the manipulation of the system, which results in nontrivial limitations on the implementation of quantum information processing tasks. Interestingly, asymmetric states can be exploited to overcome the restrictions and allow one to implement quantum information processing tasks that would otherwise be forbidden [3]. For example, in the presence of a conservation law, it is forbidden to measure exactly an observable that does not commute with a conserved quantity, but it is still possible to measure approximatively the observable with the aid of asymmetric states [4,5]. Asymmetry of states is a useful resource for implementing quantum information processing tasks [3], and the exploitation of asymmetric states has been carried out in applications, such as quantum metrology [6][7][8][9], quantum communication [10,11], and reference frame alignment [12][13][14].By taking asymmetry as a physical resource, a resource theory of asymmetry, just like the resource theory of entanglement [15], has been recently developed. The abilities of an asymmetric state to overcome the restriction imposed by a symmetry are analogous to the abilities of an entangled state to overcome the restriction of local operations and classical communication (LOCC). Asymmetric states and covariant operations in the asymmetry theory correspond respectively to entangled states and LOCC in the entanglement theory, or resource states and free operations in a general resourc...

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